Betatron-synchrotron resonance in free electron laser |
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Authors: | Yi-Jin Shi |
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Affiliation: | (1) Institute of Atomic Energy, P.O. Box 275(18), Beijing, China |
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Abstract: | In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of s=(p q)2K , p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of s=2k , but in that of s=k . The width of region of s=k is proportional to with ![epsi](/content/r1mr077125x131g2/xxlarge949.gif) (kw2/k ) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case. |
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